تقرير
Nearly Optimal List Labeling
| العنوان: | Nearly Optimal List Labeling |
|---|---|
| المؤلفون: | Bender, Michael A., Conway, Alex, Farach-Colton, Martín, Komlós, Hanna, Koucký, Michal, Kuszmaul, William, Saks, Michael |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Data Structures and Algorithms |
| الوصف: | The list-labeling problem captures the basic task of storing a dynamically changing set of up to $n$ elements in sorted order in an array of size $m = (1 + \Theta(1))n$. The goal is to support insertions and deletions while moving around elements within the array as little as possible. Until recently, the best known upper bound stood at $O(\log^2 n)$ amortized cost. This bound, which was first established in 1981, was finally improved two years ago, when a randomized $O(\log^{3/2} n)$ expected-cost algorithm was discovered. The best randomized lower bound for this problem remains $\Omega(\log n)$, and closing this gap is considered to be a major open problem in data structures. In this paper, we present the See-Saw Algorithm, a randomized list-labeling solution that achieves a nearly optimal bound of $O(\log n \operatorname{polyloglog} n)$ amortized expected cost. This bound is achieved despite at least three lower bounds showing that this type of result is impossible for large classes of solutions. Comment: 39 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.00807 |
| رقم الأكسشن: | edsarx.2405.00807 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |